How to of the Day

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• How to Use Stokes' Theorem
• How to Work With Enamel Paint
• How to Make an Authorization Letter

How to Use Stokes' Theorem Posted: 29 Jul 2016 05:00 PM PDT In vector calculus, Stokes' theorem relates the flux of the curl of a vector field ${\displaystyle {\mathbf {F} }}$ through surface ${\displaystyle S}$ to the circulation of ${\displaystyle {\mathbf {F} }}$ along the boundary of ${\displaystyle S.}$ It is a generalization of Green's theorem, which only takes into account the ${\displaystyle {\mathbf {k} }}$ component of the curl of ${\displaystyle {\mathbf {F} }.}$ Mathematically, the theorem can be written as below, where ${\displaystyle \partial S}$ refers to the boundary of the surface. ${\displaystyle \oint _{\partial S}{\mathbf {F} }\cdot {\mathrm {d} }{\mathbf {r} }=\int _{S}(\nabla \times {\mathbf {F} })\cdot {\mathrm {d} }{\mathbf {S} }}$ The true power of Stokes' theorem is that as long as the boundary of the surface remains consistent, the resulting surface integral is the same for any surface we choose. Intuitively, this is analogous to blowing a bubble through a bubble wand, where the bubble represents the surface and the wand represents the boundary. Because the wand remains the same, the surface integral will be the same no matter what the shape of the bubble is. EditSteps EditDeriving the Surface Element Consider an arbitrary vector function ${\displaystyle {\mathbf {r} }}$. Below, we let ${\displaystyle z=f(x,y).}$ ${\displaystyle {\mathbf {r} }=x{\mathbf {i} }+y{\mathbf {j} }+f(x,y){\mathbf {k} }}$ Calculate differentials. For ${\displaystyle {\mathrm {d} }{\mathbf {r} }_{x},\,y}$ is being held constant, and vice versa. We use the notation ${\displaystyle f_{x}={\frac {\partial f(x,y)}{\partial x}}.}$ ${\displaystyle {\mathrm {d} }{\mathbf {r} }_{x}={\mathrm {d} }x{\mathbf {i} }+f_{x}{\mathrm {d} }x{\mathbf {k} }}$ ${\displaystyle {\mathrm {d} }{\mathbf {r} }_{y}={\mathrm {d} }y{\mathbf {j} }+f_{y}{\mathrm {d} }y{\mathbf {k} }}$ Take the cross product of the two differentials. Surface integrals are a generalization of line integrals. A surface element therefore contains information about both its area and orientation. Thus, the goal is to compute a cross product. ${\displaystyle {\begin{aligned}{\mathrm {d} }{\mathbf {S} }&={\mathrm {d} }{\mathbf {r} }_{x}\times {\mathrm {d} }{\mathbf {r} }_{y}\\&={\begin{vmatrix}{\mathbf {i} }&{\mathbf {j} }&{\mathbf {k} }\\{\mathrm {d} }x&0&f_{x}{\mathrm {d} }x\\0&{\mathrm {d} }y&f_{y}{\mathrm {d} }y\end{vmatrix}}\\&=-f_{x}{\mathrm {d} }x{\mathrm {d} }y{\mathbf {i} }-f_{y}{\mathrm {d} }x{\mathrm {d} }y{\mathbf {j} }+{\mathrm {d} }x{\mathrm {d} }y{\mathbf {k} }\end{aligned}}}$ ${\displaystyle {\mathrm {d} }{\mathbf {S} }=(-f_{x}{\mathbf {i} }-f_{y}{\mathbf {j} }+{\mathbf {k} }){\mathrm {d} }x{\mathrm {d} }y}$ The formula above is the surface element for general surfaces defined by ${\displaystyle z=f(x,y).}$ It is important to note that the nature of surfaces (more accurately, the cross product) still allows one ambiguity - the way the normal vector is pointing. The result that we have derived applies to outward normals, as recognized by the positive ${\displaystyle {\mathbf {k} }}$ component, and for most applications, this will always be the case. EditExample 1 Find the surface integral of ${\displaystyle {\mathbf {G} }}$ over the surface ${\displaystyle z=12-4x^{2}-3y^{2}}$. The surface below has a boundary of an ellipse, not a circle. If we choose to do the surface integral, then we will need to use Jacobian change of variables in order to properly convert into polar coordinates. Therefore, we will choose to parameterize the boundary directly. ${\displaystyle {\mathbf {G} }=(2x^{2}y-4xz){\mathbf {i} }+y{\mathbf {j} }+x^{3}z{\mathbf {k} }}$ Parameterize the boundary. As always, verify that the chosen parameters work before proceeding. ${\displaystyle x={\sqrt {3}}\cos t}$ ${\displaystyle y=2\sin t}$ Calculate differentials. ${\displaystyle {\mathrm {d} }x=-{\sqrt {3}}\sin t}$ ${\displaystyle {\mathrm {d} }y=2\cos t}$ Substitute these parameters into the vector field, and take the resulting dot product ${\displaystyle {\mathbf {G} }\cdot {\mathrm {d} }{\mathbf {r} }}$. Since our boundary is on the xy-plane, ${\displaystyle z=0,}$ so cross out all terms that contain ${\displaystyle z.}$ Additionally, we are performing a closed loop integral, so our interval is ${\displaystyle [0,2\pi ].}$ ${\displaystyle {\begin{aligned}\oint {\mathbf {G} }\cdot {\mathrm {d} }{\mathbf {r} }&=\int _{0}^{2\pi }(2\cdot 3\cos ^{2}t\cdot 2\sin t\cdot -{\sqrt {3}}\sin t+4\sin t\cos t){\mathrm {d} }t\\&=\int _{0}^{2\pi }(-12{\sqrt {3}}\cos ^{2}t\sin ^{2}t+4\sin t\cos t){\mathrm {d} }t\end{aligned}}}$ Cancel out terms. The second term is 0 if we perform a u-substitution. ${\displaystyle \int _{0}^{2\pi }(-12{\sqrt {3}}\cos ^{2}t\sin ^{2}t+{\cancel {4\sin t\cos t}}){\mathrm {d} }t}$ Evaluate using any means possible. It is useful to memorize ${\displaystyle \int _{0}^{2\pi }\cos ^{2}t\sin ^{2}t{\mathrm {d} }t={\frac {\pi }{4}}.}$ ${\displaystyle -12{\sqrt {3}}\int _{0}^{2\pi }\cos ^{2}t\sin ^{2}t{\mathrm {d} }t=-3{\sqrt {3}}\pi }$ To check that this answer is correct, simply do the surface integral. The process will be longer, since you have to take the curl of a vector field and do Jacobians when you convert to the area integral. EditExample 2 Verify Stokes' theorem. Use the surface ${\displaystyle z=6-x^{2}-y^{2}}$ above the xy-plane with the given vector field below. ${\displaystyle {\mathbf {F} }=(x^{2}-2y){\mathbf {i} }+(3x-2xz){\mathbf {j} }+(x^{2}y^{2}-4yz){\mathbf {k} }}$ The goal of verification is to evaluate both integrals and check that their answers are the same. First, we will parameterize the boundary and compute the line integral. Then, we'll evaluate the surface integral. With enough practice using Stokes' theorem, you will be able to rewrite a problem into something that is easier to solve. Parameterize the boundary. When we set ${\displaystyle z=0,}$ we find that the boundary is a circle of radius ${\displaystyle {\sqrt {6}}}$ on the xy-plane. Therefore, the following parameters are appropriate. These are the components of ${\displaystyle {\mathbf {r} }.}$ ${\displaystyle x={\sqrt {6}}\cos t}$ ${\displaystyle y={\sqrt {6}}\sin t}$ Calculate differentials. ${\displaystyle {\mathrm {d} }x=-{\sqrt {6}}\sin t{\mathrm {d} }t}$ ${\displaystyle {\mathrm {d} }y={\sqrt {6}}\cos t{\mathrm {d} }t}$ Calculate the dot product ${\displaystyle {\mathbf {F} }\cdot {\mathrm {d} }{\mathbf {r} }}$. The vector field contains terms with ${\displaystyle z}$ in them, but since on the xy-plane, ${\displaystyle z=0,}$ neglect those terms. ${\displaystyle {\begin{aligned}{\mathbf {F} }\cdot {\mathrm {d} }{\mathbf {r} }&=(6\cos ^{2}t-2{\sqrt {6}}\sin t)(-{\sqrt {6}}\sin t{\mathrm {d} }t)+(3{\sqrt {6}}\cos t)({\sqrt {6}}\cos t{\mathrm {d} }t)\\&=(-6{\sqrt {6}}\cos ^{2}t\sin t+12\sin ^{2}t+18\cos ^{2}t){\mathrm {d} }t\end{aligned}}}$ Set the boundaries and simplify the integrand. Stokes' theorem tells us that ${\displaystyle t}$ is being integrated on the interval ${\displaystyle [0,2\pi ].}$ It is useful to recognize that ${\displaystyle \int _{0}^{2\pi }\sin t{\mathrm {d} }t=0,}$ which allows us to annihilate that term. Even though it is being multiplied by ${\displaystyle \cos ^{2}t,}$ that does not affect ${\displaystyle \sin t}$ being odd over the interval ${\displaystyle [0,2\pi ]}$ because ${\displaystyle \cos ^{2}t}$ is even. ${\displaystyle \int _{\partial S}{\mathbf {F} }\cdot {\mathrm {d} }{\mathbf {r} }=\int _{0}^{2\pi }(12\sin ^{2}t+18\cos ^{2}t){\mathrm {d} }t}$ Evaluate using any means possible. Here, we recognize that ${\displaystyle \int _{0}^{2\pi }\sin ^{2}t{\mathrm {d} }t=\int _{0}^{2\pi }\cos ^{2}t{\mathrm {d} }t=\pi ,}$ which, while they can be found using trig identities, are worth memorizing regardless. ${\displaystyle \int _{0}^{2\pi }(12\sin ^{2}t+18\cos ^{2}t){\mathrm {d} }t=30\pi }$ Find the surface element ${\displaystyle {\mathrm {d} }{\mathbf {S} }}$. We recall the formula converting the surface integral into an easier-to-manage area integral as ${\displaystyle {\mathrm {d} }{\mathbf {S} }=(-f_{x}{\mathbf {i} }-f_{y}{\mathbf {j} }+{\mathbf {k} }){\mathrm {d} }A.}$ In this case, ${\displaystyle f}$ refers to the surface ${\displaystyle z=f(x,y)=6-x^{2}-y^{2}.}$ ${\displaystyle {\mathrm {d} }{\mathbf {S} }=(2x{\mathbf {i} }+2y{\mathbf {j} }+{\mathbf {k} }){\mathrm {d} }A}$ Find the curl of ${\displaystyle {\mathbf {F} },}$ and compute the resulting dot product ${\displaystyle (\nabla \times {\mathbf {F} })\cdot {\mathrm {d} }{\mathbf {S} }}$. During the dot product, we find that we have three variables, yet we are integrating over just two dimensions. Simply substitute ${\displaystyle z=6-x^{2}-y^{2}}$ to solve this. ${\displaystyle {\begin{aligned}\nabla \times {\mathbf {F} }&={\begin{vmatrix}{\mathbf {i} }&{\mathbf {j} }&{\mathbf {k} }\\\partial /\partial x&\partial /\partial y&\partial /\partial z\\x^{2}-2y&3x-2xz&x^{2}y^{2}-4yz\end{vmatrix}}\\&=(2x^{2}y-4z+2x){\mathbf {i} }-(2xy^{2}){\mathbf {j} }+(5-2z){\mathbf {k} }\end{aligned}}}$ ${\displaystyle \int _{S}(\nabla \times {\mathbf {F} })\cdot {\mathrm {d} }{\mathbf {S} }=\int _{D}(4x^{3}y-8xz+4x^{2}-4xy^{3}+5-2z){\mathrm {d} }A}$ Cancel out terms. The function ${\displaystyle f(x,y)=6-x^{2}-y^{2}}$ is symmetric over both the ${\displaystyle x}$ and ${\displaystyle y}$ axes. Therefore, any terms with an odd function of either variable will cancel out. In this problem, notice that ${\displaystyle f(x,y)}$ is an even function. Therefore, we don't even need to do the multiplication for the ${\displaystyle 8xz}$ term, because ${\displaystyle 8x}$ is odd, so the entire term cancels out. This step greatly simplifies the integral to be evaluated. ${\displaystyle \int _{D}({\cancel {4x^{3}y}}-{\cancel {8xz}}+4x^{2}-{\cancel {4xy^{3}}}+5-12+2x^{2}+2y^{2}){\mathrm {d} }A}$ Simplify and convert to polar coordinates. Our problem has now been reduced to an area integral on the xy-plane, for we have taken advantage of Stokes' theorem and recognized that this "surface" - the disk on the plane - will yield the same result as our elliptic paraboloid. ${\displaystyle \int _{D}(6x^{2}+2y^{2}-7){\mathrm {d} }A=\int _{0}^{\sqrt {6}}r{\mathrm {d} }r\int _{0}^{2\pi }{\mathrm {d} }\theta (6r^{2}\cos ^{2}\theta +2r^{2}\sin ^{2}\theta -7)}$ Evaluate using any means possible. ${\displaystyle {\begin{aligned}\int _{0}^{\sqrt {6}}r{\mathrm {d} }r(8r^{2}\pi -14\pi )&=\pi \int _{0}^{\sqrt {6}}(8r^{3}-14r){\mathrm {d} }r\\&=\pi (2\cdot 36-7\cdot 6)\\&=30\pi \end{aligned}}}$ Our answer agrees with our answer obtained in step 6, so Stokes' theorem has been verified.

How to Work With Enamel Paint Posted: 29 Jul 2016 09:00 AM PDT Enamel paint is a general term applied to paints that dry to a hard, durable finish. They are an excellent choice for painting pieces that will be used outdoors or in places that are likely to be subjected to lots of wear, such as patio furniture, house trim and stairs. Working with enamel paint is a matter of knowing when it is best suited for your project, and learning where and how to apply it. EditSteps EditSelecting the Right Materials for the Job Decide if an enamel paint is right for your project. Enamel paints are best suited for use in places outdoors that are exposed to severe weather and fluctuations in temperature. They are also useful inside the home in areas that receive heavy general wear. Due to their dense, high-gloss finish, surfaces painted with enamel paints are easily cleaned and resistant to staining and damage. If the project you're working on requires a piece to be able to withstand lots of abuse, enamel paints are probably right for you.[1] Enamel paints are also a good pick for any material that needs a slick, protective finish. Bathroom fixtures and metal appliances are often finished with enamel paints. Choose the right type of paint. Traditionally, enamel paints are oil-based. The oil content allows the paint to mix and go on smoother, as well as adhere to surfaces longer. With recent increased demand for non-toxic paint alternatives, water-based enamel paints have become more common. Water-based enamel paints can be simpler to work with, as they dry faster and are easier to clean, while oil-based enamel paints last longer and provide a smoother, more durable finish.[2] The choice to use an oil-based vs. a water-based paint is largely preference. Water-based paints will do nicely for basic projects, while heavy duty oil-based paints will hold up to constant wear and harsh outdoor conditions. There exists a wide variety of enamel paints. Before buying paint, take a look at many different kinds to find the one that best suits your project. Use high quality brushes. Not just any type of brush should be used when working with enamel paints. For best results, select a brush that features the right filament type and stiffness for the paint you're using. A Chinese or ox-hair brush, for instance, is a softer-bristled brush that helps spread thick oil-based paints effortlessly. When working with water-based enamel paints, brushes made from synthetic fibers are preferable, as the filaments won't soak up the water contained in the paint and become soggy.[3] Some brushes are designed with angled bristle edges that aid in painting smoother lines. This type of brush would be ideal for working with enamel paint, which demands an even finish. Stick to one type of brush for one type of paint. For instance, while it's okay to use a synthetic filament brush with an oil-based enamel paint, it's better to choose a new brush if you've already used the synthetic brush with a water-based paint. EditApplying Enamel Paint Start with a primer. Primers are special paint products that act to prepare surfaces to be painted with a topcoat. A preliminary coat of primer will fill crevices in wood grain, cover inconsistencies in unfinished materials and give the paint a more uniform area to stick to. Most primers are oil-based, which allows them to form a better seal against the wood and helps paint hold better once the primer is dry. It is recommended that you use a coat of primer before applying enamel paint, especially on indoor surfaces, furniture, cabinets and trim.[4] Look for primers that are approved for use on the type of surface you're painting. Some brands of enamel paint are even formulated with built-in primers which improve the adhesion of the paint. Always use a primer when painting wood and other uneven natural materials, walls, cabinets, trim and any surface with variations in dimension and texture. Utilize the proper brushstroke. Because of its smooth, glossy consistency, enamel paints tend to make painting imperfections more visible. For this reason, it's advisable to use a second "tip off" stroke after brushing on the top layer of paint. To do this, make sure the brush's bristles are wet with paint (but not oversaturated) and angle the brush as you make the second pass so that only the tips run along the area that you just painted.[5][6] When using the tip off technique, make sure that you drag the brush along the entire length of the painting surface (with the natural grain if you're painting wood) to keep the thickness and orientation of each stroke uniform. Take care to make your brush strokes as fluid and even as you can. Some surfaces, such as furniture and handmade crafts, will be harder to paint than others due to their many irregular contours. Use a sprayer. Enamel paints can also be applied via sprayer, a handheld device that propels paint through tiny holes at the end of a nozzle. A sprayer will ensure that the paint goes on in even coats. Using a sprayer can save you time on jobs where there's a lot of area to cover, such as refinishing outdoor furniture and appliances.[7] A sprayer will help you quickly take care of rugged painting projects such as coating a patio deck or touching up mechanical equipment. Thicker types of enamel paint might need to be thinned before they can be used in a sprayer. [8] Apply two coats. Most home improvement experts recommend applying a second coat on projects for which enamel paints are used because of the need for protective coverage. Allow paint to dry between coats, and tip off the top coat for an even finish. Two coats of paint will be superior to a single coat for seamlessness, durability and color integrity. Use two coats of paint on stairs, outdoor work spaces and any surface that receives regular exposure to the elements. While you should apply the first coat as smoothly as possible, it's not necessary to tip it off; this process will be reserved for the outermost coat. EditDrying, Cleaning and Stripping Account for drying time. Under normal conditions, oil-based enamel paints will require between 8-24 hours to dry completely due to their thickness. Water-based paint can dry to the touch in 1-2 hours or less. Temperature and humidity have an effect on drying time, so outdoor projects can be expected to take longer to dry. Freshly painted surfaces should be left alone while drying to prevent smudging and other contact imperfections.[9] Whenever possible, time outdoor painting projects to coincide with warm, dry weather to prevent excessive humidity, temperature spikes or precipitation from potentially sabotaging the drying process. Some paint companies have special quick-drying enamel paint formulas that dry in as little as 15-20 minutes.[10] Touch up worn paint carefully. When reapplying enamel paint to worn and discolored areas, use a single thin coat at a time. Brush the fresh coat on carefully to make sure that the surface remains uniform. Primer shouldn't be needed for touch ups unless you plan on completely stripping the paint from an area first.[11] It's generally a good idea to apply a fresh coat over the entire area being painted, provided that it's not too large. This way you can avoid variations in thickness or a mismatch "seam" where the new coat has been brushed on. Clean enamel paint when needed. Another benefit of the smooth finishes created by enamel paints is that they lend themselves to hassle-free cleaning. Should a painted surface become dirty, simply wet a towel with a mixture of warm water and a mild liquid detergent and wipe away whatever debris is clinging to the paint's exterior. Oil-based enamel paints can be more difficult to clean and may require the use of mineral spirits or diluted acetone.[12] Mineral spirits is a mild solvent used to thin and strip paints. It can be brushed on or applied with a damp towel. Because of its solvent properties, mineral spirits are highly effective at removing dust and grime from dried enamel paint.[13] Remove paint using chemical paint strippers. If you need to take off a coating of paint, you will most likely need a powerful paint stripper. Chemical strippers come in a variety of forms and are one of the only methods strong enough for removing the thick, hardened paint. Apply the paint stripper in heavy globs rather than even coats and allow time for the solvent to take effect. After the chemical stripper has set to work dissolving the enamel paint, remove any remaining paint by going over the area with a medium-grit sandpaper.[14] Chemical paint strippers tend to highly caustic, and some types may emit toxic fumes. Caution should be taken when using chemical strippers to remove enamel paint yourself. If possible, acquire the services of professional paint specialists to strip surfaces finished with enamel paints. EditTips Always use a primer whenever possible before working with enamel paint. Paint that is applied without a primer base is more susceptible to running, cracking and flaking. Some enamel paints have lacquer components blended in, upping the luster and waterproofing of the glossy finish. Be sure to mask the work area with painter's tape before painting precise lines and corners. EditWarnings Chemical paint strippers are highly caustic and put off noxious fumes. Wear a mask and gloves, and work in a well-ventilated area if at all possible when dealing with chemical strippers. Avoid contact with the skin. Seek immediate medical attention if paint or chemical paint strippers get into the eyes or mouth. EditThings You'll Need Oil- or water-based enamel paint High-quality brush Paint primer Paint sprayer (optional) Painter's tape (optional) EditRelated wikiHows Become an Artist Clean Acrylic Paint Brushes Choose a Paint Brush Airbrush Change Pink Paint Into an Orange Color Paint Clean and Store Artist's Oil Brushes With Baby Oil EditSources and Citations Cite error: <ref> tags exist, but no <references/> tag was found

How to Make an Authorization Letter Posted: 29 Jul 2016 01:00 AM PDT An authorization letter gives a third party permission to act on your behalf, especially in instances when you may be unavailable or unable to act for yourself. You may need someone to assist you, for example, with your financial matters, legal issues, or health directives. A properly written authorization letter will accomplish this. EditSteps EditSample Authorization Letters Sample Financial Authorization Letter Sample Health Authorization Letter Sample Legal Authorization Letter EditPreparing to Write an Authorization Letter Understand what an authorization letter does. An authorization letter gives another person the right to act on your behalf in specific matters. They are primarily used in circumstances in which the letter writer is not able to represent themselves. A few examples of situations that may require an authorization letter include: A parent or guardian may grant child care workers authorization to make basic emergency medical decisions regarding the children in their care.[1] It is advisable to give an authorization letter for minors traveling with adults who are not their parents or guardians. This will protect the minor from child trafficking and child custody issues.[2] If you have money held in a regional bank that you can no longer easily access, you may need to write a letter of authorization to allow someone else to handle issues that arise with the account or financial institution. An authorization letter can allow release of personal information, such as medical records.[3] You may also need to authorize another party to act on your behalf to handle especially fast-moving financial transactions. Not every business deal can wait for you; if you are temporarily indisposed, you can write a letter of authorization and temporarily grant decision-making powers to a trusted colleague. Identify the different parties involved in an authorization letter. There are three parties involved in an authorization letter. The first party is the original rights holder, such as the parent of a child or the owner of a bank account. The second party is the group or individual with whom the first party is conducting a transaction, such as a financial institution or hospital. The third party is the person selected to act as a proxy in the first party's absence. The letter should be addressed to the second party. The letter will explain the rights granted to the proxy who will be acting in your place.[4] If the second party is not known (especially in cases where authority was granted for potential emergency situations), you will have to address the letter simply "To whom it may concern." Type your authorization letter rather than writing it by hand. A handwritten letter may be difficult to read and isn't as professional in appearance as a typed letter. The authorization letter is an important document authorizing someone to hold your legal or financial powers for you. It must be prepared to meet scrutiny. If someone else close to you wants to dispute the authority of the letter holder, the document may be used as evidence in a court of law. EditWriting the Letter's Heading Place your name and address on the top left side of the page. Follow the standard format of a business letter. Your name should be on the first line, your street information on the second line, and your city, state and zip code on the third line. All lines (including those that follow) should be single spaced.[5] Include the date. After your name and address, skip one line and place the current date on the next line. Write out the full date (such as February 2, 2015, for example). Do not abbreviate the date. Write the recipient's name and address next. Leave one blank line between the date and first part of the recipient's name and address. The receiver's information should be in the same format as your information. Keep in mind that the recipient is not the same as the one authorized to make decisions for you. You are granting authority to a third party (a proxy) to act on your behalf, but the letter should be addressed to second party (the one with whom you and your proxy are dealing).[6] You may have to leave this portion blank if you do not know the party with which you will be dealing. For example, if you have granted emergency medical powers over your child to a child care worker in case you cannot be reached, you may not know which hospital your proxy will have to deal with. EditWriting the Body of the Letter Write the salutation. Use the appropriate titles, such as "Dr.," "Ms.," "Mrs.," or "Mr.," rather than using first names. The salutation may open with "Dear," or more formally just the word "To." Use the full name and title of the person to whom the letter is addressed. If you do not know the specific name of the party with whom your proxy will be dealing, write "To whom it may concern." Keep the authorization letter short and precise. Longer letters will include more information that can be interpreted in different ways. Brief letters that specifically address the matter with as little extra verbiage as possible are less likely to lead to conflicting interpretations. Specify the duties that your representative is authorized to do on your behalf. Make sure your authorization letter is concise and precise. You need to give specific details about the authorization you are granting. For example, your representative can authorize a medical procedure, sign legal documents in your absence, or withdraw funds from your bank. For example, start out the authorization letter with: I, (insert your full name), hereby authorize (insert proxy's full name) to release to (insert the organization that will receive your medical records), the following medical information from my personal medical records: (list the medical information here).[7] Give very specific details for this authorization. If the letter is regarding your medical information, include your medical insurance number and claim information. If you need assistance regarding a legal matter, include the case number. For financial matters, include the applicable account information. Give the dates for the authorization. Specify when this authorization is in effect. Give the beginning and ending dates. For example, you might write, "The proxy has authorization to make medical decisions for my child while staying at (address) from September 1, 2015 to September 15, 2015." In some cases, you may be unsure of the dates, such as if you are authorizing in case of an emergency. For this type of authorization, specify a length of time. For example, you might write, "In the event of an emergency, the proxy has authorization to act on my behalf for 30 days." Give the reason for the authorization. Explain why you need a representative to act on your behalf. The explanation might indicate that you are ill, out of town, or may not be able to be reached for certain periods of time. Explain any restrictions on the authorization. You may also want to identify the areas that you are not authorizing. For example, you might say that the proxy is not allowed to use your medical information for any other purpose than specified in the letter. Or, you might say that the proxy is not allowed to make certain financial decisions on your behalf without prior written consent.[8] Conclude the letter. Finish up the letter with a closing word such as "Sincerely." Leave four blank lines, which is where you'll put your handwritten signature, and then type your full name. EditFinalizing the Letter Format the letter properly. A letter of authorization is a business letter and should be formal in tone and format. Standard business letters use a block format. The body should be single-spaced, and there should be no indentation of the paragraphs. Instead a blank line between the salutation and the first paragraph as well as between paragraphs.[9] Find a witness or notary public. A witness is someone who will observe you signing the authorization letter. This ensures that you are not signing the letter under duress, and that you are in fact the person giving the authorization. In some instances, it is a good idea to have your letter notarized by a notary public.[10] This person is someone authorized by your state to attest to legal documents. This person should not be anyone named in the letter. Sign the letter. Print out the letter and sign it with blue or black ink. You may choose to include a date line next to your signature. If so, write the date that you sign the document. Have your witness sign and date the letter as well, or ask the notary public to notarize the letter. Give the original letter to the proxy. In most cases, the proxy will retain the letter so that he or she has proper documentation of authority granted. The proxy may need to present the letter to immigration officials, for example, if he is traveling internationally with your child. Keep a copy of the letter. Make sure to retain a copy of the letter for your records. You may need to produce it if any questions arise regarding the authorization you've given to your proxy. EditTips If you need to make any changes (additions or deletions) to the letter of authorization, it is recommended that you write a new letter of authorization and get it notarized or witnessed.[11] EditRelated wikiHows Write a Bank Authorization Letter Write a Letter of Permission Write a Guarantor Letter Write a Medical Release Letter Get Power of Attorney EditSources and Citations Cite error: <ref> tags exist, but no <references/> tag was found

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